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IntMath Newsletter: radius of curvature, log curve, free math videos

By Murray Bourne, 23 Jul 2010

22 Jul 2010

In this Newsletter:

1. Math of the great summer brain drain
2. Math tip: Radius of Curvature, an application of differentiation
3. Slope of the logarithm curve at any point
4. Friday math movie - Khan's Academy
5. How to import GeoGebra files into JSXGraph
6. Final thought – stay positive

1. Math of the great summer brain drain

Here is some interesting information about how forgetting works, and what we can do to reduce it.

Do you want to be a successful math student? This could be a good place to start.

Suitable for: Everyone.

forgetting

Everyone knows students drop a few grades in their knowledge during the summer months. What's the math behind this?

Read more: Math of the great summer brain drain

2. Math tip: Radius of Curvature, an application of differentiation

I re-wrote a page on Interactive Mathematics recently and thought you may find it useful.

A reader sent in a question asking how to find the radius of curvature if we don't know the function. I solve this problem in 3 different ways. You can get some good mathematical understanding from this.

Suitable for: Everyone. Even if you have never heard of calculus yet, you will come across it one day and this example gives you an idea about what it can be used for.

Summary of the page:

  • What is radius of curvature and why study it?
  • Example of radius of curvature involving a cubic curve
  • Exploration of radius of curvature using an interactive graph
  • A second example (the one sent in by a reader) that is solved in 3 different ways:
    1. Using a parabola to model the data and differentiation
    2. Using linear approximations and concepts of calculus
    3. Using the formula for the circle passing through 3 points

So here it is:

train tracks radius of curvature

In this example, we learn about radius of curvature and one of its applications.

Read more: Radius of Curvature

3. Slope of the logarithm curve at any point

Suitable for: Everyone. Once again, this example involves differentiation (a calculus topic), but the main concept is easy for everyone to understand: as you move around a curve, the slope changes.

Geogebra to JSXGraph

This is a new interactive graph in IntMath. You can drag a point around a logarithm curve to learn about the changing slope.

You'll laso learn what a log curve looks like.

Learn more: Slope of the Logarithm Function

4. Friday math movie - Khan's Academy

Suitable for: Everyone.

Khan Academy

Here's a wide range of free videos by a guy that clearly loves to teach. This is a very popular math video series.

Watch a typical video. This one is about the Unit Circle:

Friday math movie – free math videos by Khan Academy

5. How to import GeoGebra files into JSXGraph

Suitable for: Math computer geeks.

JSXGraph and Geogebra

This article explains how you can create interactive math applets using GeoGebra (which is easy) and import those files into JSXGraph (which displays the math in a browser, and is cross-platform and cross-browser).

Read more: How to import GeoGebra files into JSXGraph

6. Final thought – stay positive

A lot has been written about the power of positive thinking. But it's true!

The people who have a negative approach to math ("This is dumb!" "This is never used in the real world!") and do nothing much to improve their skills, get into a cycle where they get worse.

Here's a thought from self-help speaker and author Brian Tracy:

"The more positive you are when you think and work toward your goals, the faster you achieve them." [Brian Tracy]

Until next time, enjoy whatever you learn.

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